Quantum zeno effect of general quantum operations

In this paper, we show that the quantum Zeno effect can occur for generalized quantum measurements or operations. As a consequence of frequently performing nonselective measurements (or trace-preserving completely positive maps), the evolution of a certain measurement-invariant state is governed by an effective Hamiltonian defined by the measurement (or map) and the free-evolution Hamiltonian. For selective measurements, the state may change randomly with time according to measurement outcomes, but some physical quantities (operators) still evolve according to the effective Hamiltonian.